Questions: Use a graphing calculator to find the corresponding y-values of the function for the values x=-2,-1,0, and 2. Round your answer to two decimal places, if necessary. If the y-value is undefined, write Und. f(x)=3+5x-5x^2

Use a graphing calculator to find the corresponding y-values of the function for the values x=-2,-1,0, and 2. Round your answer to two decimal places, if necessary. If the y-value is undefined, write Und. f(x)=3+5x-5x^2
Transcript text: Use a graphing calculator to find the corresponding $y$-values of the function for the values $x=-2,-1,0$, and 2 . Round your answer to two decimal places, if necessary. If the $y$-value is undefined, write Und. \[ f(x)=3+5 x-5 x^{2} \]
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Solution

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Solution Steps

Step 1: Evaluate \( f(-2) \)

Substituting \( x = -2 \) into the function: \[ f(-2) = 3 + 5(-2) - 5(-2)^{2} = 3 - 10 - 20 = -27 \]

Step 2: Evaluate \( f(-1) \)

Substituting \( x = -1 \) into the function: \[ f(-1) = 3 + 5(-1) - 5(-1)^{2} = 3 - 5 - 5 = -7 \]

Step 3: Evaluate \( f(0) \)

Substituting \( x = 0 \) into the function: \[ f(0) = 3 + 5(0) - 5(0)^{2} = 3 + 0 - 0 = 3 \]

Step 4: Evaluate \( f(2) \)

Substituting \( x = 2 \) into the function: \[ f(2) = 3 + 5(2) - 5(2)^{2} = 3 + 10 - 20 = -7 \]

Final Answer

For \( x = -2 \), \( y = -27 \) \\ For \( x = -1 \), \( y = -7 \) \\ For \( x = 0 \), \( y = 3 \) \\ For \( x = 2 \), \( y = -7 \)

Thus, the answers are:

  • \( f(-2) = \boxed{-27} \)
  • \( f(-1) = \boxed{-7} \)
  • \( f(0) = \boxed{3} \)
  • \( f(2) = \boxed{-7} \)
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